- #1
thatboi
- 127
- 18
Consider a generic Hermitian 2x2 matrix ##H = aI+b\sigma_{x}+c\sigma_{y}+d\sigma_{z}## where ##a,b,c,d## are real numbers, ##I## is the identity matrix and ##\sigma_{i}## are the 2x2 Pauli Matrices. We know that the eigenvalues for ##H## is ##d\pm\sqrt{a^2+b^2+c^2}## but now suppose I have the matrix ##\tilde{H} = (\sigma_{x} \otimes A) + (\sigma_{y} \otimes B) + (\sigma_{z} \otimes C)## , where ##\otimes## denotes the Kronecker product and ##A,B,C## are now N x N diagonal matrices with diagonal entries ##a_{i},b_{i},c_{i}## respectively. I'm wondering if there is some nice generalization of the 2x2 eigenvalue formula in my first statement? I feel like there must be.